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## ganeshie8 one year ago Just want to share this neat idea for why $$-\times-=+$$

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1. karatechopper

oh oh oh go I'm listening! :D

2. anonymous

spit that fire

3. ganeshie8

let $$r_1$$ and $$r_2$$ be two positive numbers, then : $\large (-r_1)(-r_2) = (r_1e^{i\pi})(r_2e^{i\pi})=r_1r_2e^{i2\pi}=r_1r_2$

4. anonymous

neat idea, thanks

5. ikram002p

that wouls also explain why -×+=- i loved it

6. ganeshie8

didn't want to add anything as it looks so elegant+complete as an one liner xD But here some explanation : To multiply two complex numbers, we simply "multiply the two lengths" to get the resulting length and "add the two angles" to get the resulting angle. $(r_1,\theta_1)*(r_2,\theta_2)=(r_1r_2,~\theta_1+\theta_2)$ Next notice that the angle for any negative number is $$\pi$$ as they fall on the negative real axis. Consequently, multiplying two negative numbers adds up the angles$$(\pi+\pi)$$ taking the result to positive real axis.

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